Utilizing the electron emission from carbon nanotubes, carbon fibers or other columnar narrow carbon structures, one can build a transistor based on a diode, triode or even higher order transistor structure (e.g., pentode).
Generally, the columnar narrow and sharp carbon structures such as fibers, tubes, etc., have a length of over 2 micrometers and sometimes can achieve lengths over 10 micrometers. In order to utilize the field emission properties of these carbon films, one needs to create cavities, around which the transistor structures are built and a certain low-pressure environment or vacuum is held.
An example is given by A. A. G. Driskill-Smith, D. G. Hasko, and H. Ahmed (“The ‘nanotriode:’ A nanoscale field-emission tube”, Applied Physics Letters, Vol. 75, Number 18, Nov. 1, 1999, p. 28451) where they show the fabrication sequence of a nanotriode made on a tungsten (W) wafer. They also show how this type of device can be used as a transistor where the gate modulates the current that goes to the anode. In this example, the triode was built up on the tungsten wafer. This requires many different deposition layers, some of which can be quite thick. The scale of the device shown is less than 1 micron which will not accommodate long carbon nanotube structures that are longer.